Subgroups — #15756689

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114995	C₂	1	2	yes	maximal
2	#13114992	C₂	1	2	yes	maximal
3	#13114964	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#384	C₂²	1	2	yes	—
8	C₂×#88048	—	2	4	no	—
9	C₂×#88047	—	2	4	no	—
10	#11718596	C₂²	1	2	yes	—
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	C₁₃×#340	—	2	2	no	—
14	#11718143	—	2	2	no	—
15	C₈×#1055	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₃	D₄	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₃	—	2	2	no	—
22	C₂×C₄⋊Dic₁₃	—	2	2	no	—
23	C₂×C₄⋊Dic₁₃	—	2	2	no	—
24	C₂²×#1055	D₄	1	2	yes	—
25	C₂²×#1055	D₄	1	2	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₄×C₈×C₁₃	Q₈	1	2	yes	—
28	#88048	—	4	8	no	—
29	#88047	—	4	8	no	—
30	C₄×#1055	C₂×C₄	1	2	yes	—
31	C₄×#1055	C₂×C₄	1	2	yes	—
32	C₄×#1055	Q₈	1	2	yes	—
33	C₄×#1055	Q₈	1	2	yes	—
34	#8814	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	—	4	2	no	—
36	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂²×Dic₁₃	—	4	2	no	—
40	C₂×C₈×C₁₃	—	2	4	no	—
41	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
42	C₁₃×C₄⋊C₄	—	4	4	no	—
43	C₁₃×C₄⋊C₄	—	4	4	no	—
44	C₁₃×C₄⋊C₄	—	4	4	no	—
45	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₄⋊Dic₁₃	—	4	4	no	—
50	C₄⋊Dic₁₃	—	4	4	no	—
51	C₄⋊Dic₁₃	—	4	4	no	—
52	C₂×#1055	C₄⋊C₄	1	4	yes	—
53	C₂×#1055	C₄⋊C₄	1	4	yes	—
54	C₂×#1055	D₈	1	4	yes	—
55	C₂×#1055	SD₁₆	1	8	yes	—
56	C₂×#1055	Q₁₆	1	4	yes	—
57	#1845	—	13	2	no	—
58	#1844	—	13	2	no	—
59	#1834	—	13	1	no	—
60	#1834	D₁₃	1	1	yes	characteristic
61	C₂×C₈²	—	13	1	no	—
62	C₂³×C₁₃	#127	1	1	yes	characteristic
63	C₂×C₄×C₁₃	—	8	2	no	—
64	C₂×C₄×C₁₃	—	8	2	no	—
65	C₂×C₄×C₁₃	—	8	2	no	—
66	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
74	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
75	C₂×C₄×C₁₃	#135	1	4	yes	—
76	C₂×Dic₁₃	—	8	2	no	—
77	C₂×Dic₁₃	—	8	2	no	—
78	C₂×Dic₁₃	—	8	2	no	—
79	C₈×C₁₃	—	2	4	no	—
80	#1055	#106	1	8	yes	complemented
81	#1055	#107	1	8	yes	complemented
82	C₂×#107	—	26	4	no	—
83	C₂×#106	—	26	4	no	—
84	C₂×C₄×C₈	—	13	1	no	—
85	C₂×C₄×C₈	—	13	1	no	—
86	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
87	#384	—	13	2	no	—
88	#384	C₂×D₁₃	1	2	yes	—
89	#340	—	2	2	no	—
90	#340	—	26	2	no	—
91	C₈²	—	13	4	no	—
92	C₂²×C₁₃	#384	1	1	yes	characteristic
93	C₂²×C₁₃	#492	1	2	yes	—
94	C₂²×C₁₃	#493	1	1	yes	characteristic
95	C₂²×C₁₃	#494	1	1	yes	characteristic
96	C₂²×C₁₃	#495	1	2	yes	—
97	C₄×C₁₃	—	16	2	no	—
98	C₄×C₁₃	C₂×#106	1	2	yes	—
99	C₄×C₁₃	C₂×#107	1	2	yes	—
100	C₄×C₁₃	#427	1	2	yes	—
101	C₄×C₁₃	#498	1	2	yes	—
102	C₄×C₁₃	#499	1	2	yes	—
103	C₄×C₁₃	#500	1	2	yes	—
104	Dic₁₃	—	16	2	no	—
105	C₂²×C₈	—	13	2	no	—
106	C₂²×C₈	—	13	2	no	—
107	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
108	C₂×C₄⋊C₄	—	2	2	no	—
109	C₂×C₄⋊C₄	—	2	2	no	—
110	C₂×C₄⋊C₄	—	2	2	no	—
111	C₂×C₄⋊C₄	—	26	2	no	—
112	C₂×C₄⋊C₄	—	26	2	no	—
113	C₂×C₄⋊C₄	—	26	2	no	—
114	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
115	#107	—	52	8	no	—
116	#106	—	52	8	no	—
117	C₄×C₈	—	13	2	no	—
118	C₄×C₈	—	13	2	no	—
119	C₄×C₈	—	13	2	no	—
120	C₄×C₈	—	13	2	no	—
121	C₄×C₈	Dic₂₆	1	2	yes	—
122	C₄×C₈	C₄×D₁₃	1	2	yes	—
123	C₂×C₁₃	#1706	1	2	yes	—
124	C₂×C₁₃	#1707	1	2	yes	—
125	C₂×C₁₃	#1844	1	1	yes	characteristic
126	C₂×C₁₃	#1845	1	1	yes	characteristic
127	C₂×C₁₃	#1846	1	1	yes	characteristic
128	C₂²×C₄	—	4	2	no	—
129	C₂²×C₄	—	52	2	no	—
130	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
131	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
132	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
133	C₂×C₈	—	2	4	no	—
134	C₂×C₈	—	13	4	no	—
135	C₂×C₈	—	13	4	no	—
136	C₂×C₈	—	13	4	no	—
137	C₂×C₈	—	13	8	no	—
138	C₂×C₈	—	13	4	no	—
139	C₂×C₈	#6101	1	4	yes	—
140	C₄⋊C₄	—	4	4	no	—
141	C₄⋊C₄	—	4	4	no	—
142	C₄⋊C₄	—	4	4	no	—
143	C₄⋊C₄	—	52	4	no	—
144	C₄⋊C₄	—	52	4	no	—
145	C₄⋊C₄	—	52	4	no	—
146	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
147	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
148	C₄²	Q₈×D₁₃	1	1	yes	characteristic
149	C₄²	Q₈×D₁₃	1	1	yes	characteristic
150	C₁₃	#8814	1	1	yes	characteristic, complemented, Sylow
151	C₂³	#88194	1	1	yes	characteristic
152	C₂×C₄	—	8	2	no	—
153	C₂×C₄	—	8	2	no	—
154	C₂×C₄	—	8	2	no	—
155	C₂×C₄	—	104	2	no	—
156	C₂×C₄	—	104	2	no	—
157	C₂×C₄	—	104	2	no	—
158	C₂×C₄	#88142	1	1	yes	characteristic
159	C₂×C₄	#88142	1	1	yes	characteristic
160	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
161	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
162	C₂×C₄	D₈×D₁₃	1	2	yes	—
163	C₂×C₄	SD₁₆×D₁₃	1	4	yes	—
164	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
165	C₂×C₄	C₂×#6101	1	1	yes	characteristic
166	C₂×C₄	#88198	1	1	yes	characteristic
167	C₂×C₄	#88204	1	4	yes	—
168	C₈	—	2	4	no	—
169	C₈	—	13	8	no	—
170	C₈	—	13	8	no	—
171	C₂²	#11718637	1	1	yes	characteristic
172	C₂²	#11718720	1	2	yes	—
173	C₂²	#11718812	1	1	yes	characteristic
174	C₂²	#11718836	1	2	yes	—
175	C₂²	#11718842	1	1	yes	characteristic
176	C₄	—	16	2	no	—
177	C₄	—	208	2	no	—
178	C₄	#11718516	1	2	yes	—
179	C₄	D₁₃×#106	1	2	yes	—
180	C₄	#11718535	1	2	yes	—
181	C₄	D₁₃×#107	1	2	yes	—
182	C₄	#11718659	1	2	yes	—
183	C₄	#11718725	1	2	yes	—
184	C₂	#13114427	1	2	yes	—
185	C₂	#13114432	1	2	yes	—
186	C₂	#13114991	1	1	yes	characteristic
187	C₂	#13114994	1	1	yes	characteristic
188	C₂	#13114998	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88194
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1834	C₂
socle, prime radical	C₂³×C₁₃	#127
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1834	D₁₃
hypocenter	C₁₃	#8814
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
15. C₈×#1055	C₄	semidirect
80. #1055	#106	semidirect
81. #1055	#107	semidirect
150. C₁₃	#8814	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13114995	2
#13114992	2
#13114964	2
C₂×C₈×#1055	2
C₁₃×#1834	2
#8814	13